Rules: Derivative of Sums, Products & Quotients of Functions

Linearity

Linearity of the derivative (derivative of sums of functions).

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 3 on page 3

The Liebniz Rule / Product Rule

Product rule for derivatives. Gives proof sketch.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 4 on page 3

The Quotient Rule

Quotient rule for derivatives, derived using product rule.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 5 on pages 3–4

Product Rule Example

Product rule used to find a derivative.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 1 on page 1

Logarithmic Differentiation

Finding the derivative of a product of functions using logarithms to convert into a sum of functions. Includes worked example.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 5 on pages 4–5

Differentials

Differential notation for derivatives is explained and common rules for derivatives are listed in differential notation. Includes an example of a derivative taken in differential notation.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Read lecture notes, section 1 on pages 1–2

Derivatives of Combinations of Functions

Rules for the derivatives of sums and products of functions, as well as the chain rule and rules for finding the derivative of an inverse function.

• 18.013A Calculus with Applications, Spring 2005
  Prof. Daniel J. Kleitman

Course Material Related to This Topic:

• Read chapter 8 of online textbook

Derivatives of Exponential and Trigonometric Functions

Taking the first and second derivatives of a function involving an exponential and a cosine.

• 18.01 Single Variable Calculus, Fall 2005
  Prof. Jason Starr

Course Material Related to This Topic:

• Complete practice problem 4 on pages 2–3
• Check solution to practice problem 4 on pages 9–10

Evaluating Derivatives and Limits

Four-part question involving the evaluation of three derivatives and a limit.

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

• Complete exam problem 1 on page 1
• Check solution to exam problem 1 on page 1

Evaluating Derivatives

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

Two questions finding the derivatives of functions.

• Complete exam problems 1 to 2 on page 1
• Check solution to exam problems 1 to 2 on page 1

Finding the derivatives of four functions.

• Complete exam problem 2 on page 1
• Check solution to exam problem 2 on page 1

Three derivatives to be evaluated using a variety of techniques.

• Complete exam problem 1 on page 1
• Check solution to exam problem 1 on page 1

Differentials and Indefinite Integration

Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.

• 18.01 Single Variable Calculus, Fall 2006
  Prof. David Jerison

Course Material Related to This Topic:

• Complete exam problems 3A–1 to 3A–3 on page 21
• Check solution to exam problems 3A–1 to 3A–3 on pages 37–9